Equalizer



AWM 'mmm F. W. Mmmm-11 EQUALLZER 2 sheets-Smm 2 Filed March 23,1939

ATTORNEYS Patented Apr. 8, 1941 UNITED STATES-'PATENT OFFICE EL... i t

Paul W. Klipsch, Houston, Tex., assigner to Esme E. Rosaire, Houston,Tex.

Application March 23, 1939, Serial N0. 263,614 s claims. ii. 17a-44)This invention relates to wave transmission networks, particularly toequalizer networks hav ing adjustable attenuation characteristics.

An object is to provide an adjustable equalizer network having an imageimpedance which is a constant resistance for all adjustments of equal#ization and one in which the amount of equaliza tion may readily beadjusted with a minimum number of Variables.

Another object is to provide an equalizer with a minimum number ofreactive elements and in which the only variable elements are pureresistances.

` `Another object is to provide an equalizer in which both `ends of afrequency spectrum may simultaneously and practically independently beequalized, compensated or predistorted.`

A further object is to form a simple equalizer whose complementarycircuit is as readily eonstructed, and such that a given equalizer andits 'A' Fig. 1 shows a form of a lcircuit adapted to transmit the lowfrequencies lwith less atte'nuaf tionl than the restof the spectrum.

Fig. 2 shows a family of performance curves for the circuit of Fig. 1for different amounts of equalization. I

Fig. 3 shows ar circuit adapted tov attenuate the high frequencies lessthan the remainder of the spectrum. a

Fig. 4 shows a circuit for attenuating both the high and low frequencies'by adjustable predetermined amounts less than the rest of the spectrum.

Fig. 5 is a graphical illustration of the performance of the circuit ofFig. 4. 'f

Fig. 6 is a circuit which generalizes the nven tion by the use of buttwo impedances.

Fig. 7 -isthe H section equivalent of Fig. 6.

Figs. 8 and 9 are the lattice equivalents of Fig. 6.

Fig. 10 depicts two equalizers used to extend the range of a single one.Fig. 11 graphically shows the performance of equalizers as depicted inFig. 10 where each of the equalizers is of the form of Fig. 1, but whosemidfrequencies are not equal.

Fig. 12 `shows an alternative form of the invention involving atransformer. `.The following list of symbols will j=frequency. u l p ,lf1=mldfrequency for low-pass.

be used:

Fig.`1 shows a form of the invention, an equalizer to boost the lowfrequencies (hence referred to as a low-pass type) with input terminalsI and 2 and output terminals 3 and 4. When operated betweenresistancesRo there are no reflection lossesat vthe terminals. f i

' In'Figs. 1, 3, 4, and 6, the resistor combination .1/2R11, R21constitutes a simple T attenuator. The

values of R11 and R12 are determined from the line impedance andthetotal loss. Thus I 4 "yzRnzRo (l) @FROM 2) where am is themaximum lossin nepers due to the unbridged T and Ro is the characteristic impedance.l c

A convenient table for the determination of R11 and R21 is to be foundin a paper by P. K. McElroy in Proceedings Institute of RadiovEngineers, vol.'23, pages 213-233, March 1935. As an example,` suppose10 decibels loss is desired and the pad is to be used between 500 ohmterminations; p The base lossv or maximum attenuation is lRi|=5ootsunami '-1260 ohms The values L12 and C22 in Fig. 1 are determined fromRo L12-??1 (3) where f1 is the frequency at which approximately half theequalization is attained, and is herein called the mid-frequency.

An alternative to and exact equivalent of the R11, R21 T pad is thebridged T shown by McElroy (mentioned above) in his Fig. 5, page 222,and table VII, page 233.

The adjustable resistors R12 and R22 are related itl-312:1@

Table I 95 a R12 R22 Correction decibels nepr R12/R0 ohms ohms m 3. 721, 86o 135 1. 21 i 557 412 D. 394 197 1, 270

Since the circuit of Fig. 6 is the generalized circuit of Fig. 1 andsince the circuits lof Figs. 6 and 8 are equivalent, the total insertionloss is giveny by the constant R lattice equation where ZA in Fig. 8 isthe impedance of 1/zlitn in parallel with 1/2Z12 and l/2R12 in series inFig. 6 and I* is the transfer constant defining the loss and phaseangle. Note that (7) defines both the transfer constant and totalinsertion loss when there are no reiiection losses, that is when thenetwork is operated between terminal impedances equal to Ro.

Using Equation 7, the performance of the circuit of Fig. 1 is computedand shown in Fig. 2, in which curves of loss against reactance areplotted for different values of R12.

Fig. 3 is the high-pass counterpart of the klowpass circuit of Fig. l.It may be made complementary thereto whereby the sum of the losses ofthe circuits of Figs. 1 and 3 are substantially constant by properchoice of the value of f2, thereby making, in combination with thecircuit of Fig. 1, a convenient predistorting-restoring network. Itsperformance may be found from Fig. 2 simply by using the reciprocal ofthe abscissa. Equations 1, 2 and 5 to '7 are applicable. Equations 3 and4 are applicable to Fig. 2 if L22 is written for L12 and C12 for C22.

Obviously more complicated impedances than, for example, L12, C22 inFig. 1 may be used. Resonant and anti-resonant circuits and multiplebranch impedances may be employed, and the simplicity oi the variablefeature will be retained. Fig. 6 illustrates the invention in thisbroader form. The design of such impedances may be accomplished by theuse of such references as Everitts Communication Engineering McGrawHill, 1932, 1937, a book, Chapter IX, and the references given therein,Equations 1, 2, and 5 to 7 still apply, and suitable impedance designmay be substituted for (3) and (4) see also A reactance theorem, R. N.Foster, Bell System Technical Journal, vol. III, No. 2, April 1924.

As an example of such an elaboration, suppose Z12 is a reactance in theform of an induotance L12 in series with a capacitance C12. Theresulting performance will be a certain maximum loss with a dropy to asmaller loss at a frequency f1 determined by the product L12-C12. Thecorrection at f1 will be cam-an and the width of the resulting pass bandor the stepness of the loss-frequency curve for a given set of valuesam, an will be determined by the ration L12/C12. Still another type ofimpedance Z12 would result from the two terminal impedance of a reactiveladder with resistance or reactance termination. The impedance in such acase would not be a nearly pure reactance, but would contain a largerdissipative component than when nearly pure reactive elements are used.

Fig. 4 is a combination high-pass and low-pass equalizer by means ofwhich both ends of a spectrum may be boosted relative to the middlesomewhat in the same way that the circuits of Figs. 1 and 3 wouldperform in tandem, but the .total base insertion loss is that of asingle circuit only. In the case of Fig. 4 however the equalization isaccomplished with resonant and anti-resonant circuits whereby theperformance curve slopes are made more steep and the losses increasebeyond the limits of 50 and 8000 cycles. The high and low ends may beequalized substantially independently if the mid-frequencies f1 and f2are separated a suiiicient amount.

Fig. 5 is the performance of the circuit of Fig. 4 where the low-passmid-frequency (f1) is 50 cycles, the high-pass mid-frequency (f2) is8000 cycles, the pad loss, am, is 10 decibels, and the values of R12,R22 and R13, R23 are chosen from Table I.

The numerical values 0f L12, C12, L22, C22 etc. for Fig. 4 may becomputed from (3) and (4) and for the example given where f1=50,f2=8000, v

and Rar-500 ohms they are:

' Table II L12=0.795 henry C12=12.5'7 2f. L22=3.18 henry C22: 3.19 2f.L13=0.005 henry C13: 0.08 2f. L2a=0.020`henry C23: 0.02 pf.

.And the values of R12, R22 and R13, R23 are given in Table I.

It should be understood that the numerical values given are not intendedto limit the scope of the patent, but to serve as illustrations ofcomputation by means of the various equations given.

Whatever the nature of Z12, it is necessary that Z22 be inverse thereto.Thus in order that the network of Fig. 6 have an iterative or imageimpedance which is a constant resistance it is necessary that Z12and Z22be inverse, that is that they be related by g It may be noted that inFig. 1 this requirement .iS met since l y JLLLLh-g50) Cj22.1%02

Thus the determination of Ziz by whatever design procedure is employedis suiiicient also to determine Z22. Inverse networks are discussed. andthe method of their :derivation shown by T. E. Shea TransmissionNetworks and Wave Filters, vanNostrand, 1929, chapter 5,

Obviously, the circuits of Figs. 1, 3 and 4 may bemade into networkswhich are balanced and symmetrical with respect to ground simply bytransforming them into their equivalent lattices or H sections. Thisprocedure is well known ,(Bartlett, A. C., Phil Mag. 4, pages 902-907,Nov. 1927) for lattices and is obvious for H sections. Fig'. 9 shows alattice which is equivalent to the `bridged T of Fig. 6, and Fig. 8shows the generalization of Fig. 9. Fig. 7 shows the balanced bridged Hwhich is equivalent to the bridged T of Fig. 6. A still further possibleequivalent configuration consists in the reduction of the lattice ofFig. 49 or Fig. 8 to a bridged T containing a transformer t as shown inFig. 12.

Fig. 12 illustrates an equivalent of Fig. 4 when ZZA is equal to theimpedance of terminals I and 3 of Fig. `4 (terminals 2 and 4 not beingconnected) and ZB is equal to the shunt arm plus 1/2l7t11 of Fig. 4. Bysimilar reasoning Fig. 8 is the equivalent of Fig. 4 when ZA and ZB havethe same meanings as defined above for Fig. 12. Development of Fig. 4into a balanced H consists simply of creating a mirror image of Fig. 4below the line between terminals 2, 4 whereby the line between terminals2, 4 becomes a neutral which may be retained or eliminated as desired.

The circuits shown, when designed according to the equations herewith,are characterized by an image impedance which is a constant resistanceat all frequencies so that the real part of the transfer constant isequal to the total insertion loss when a given circuit is operatedbetween terminations having the same image impedance.

Depending upon the degree of linearity demanded, the attenuation of thecircuit of Fig. 1 is linear over a range of two or three octaves. Byusing a plurality of such equalizers with their mid-frequencies fia,fit, etc. spaced at two to four octave intervals, the linear range maybe extended over any desired frequency range. Fig. 10 shows two unitscascaded, and Fig. 11 shows the results of cascading where curve IIshows the linear range l. r.1, curve I2 shows the performance of a unitwith a mid-frequency fit greater than fia by the amount of the linearrange, and curve I3 shows the sum of curves II and I2 produced by thecascaded units. The linear range l. r.2 of the combination is roughlytwice the value of l. r.1.

The invention claimed is:

1. A constant resistance variable attenuation equalizer comprising adissipative T network, two arms comprising reactances X12 and X13bridging said T, variable resistances R12 and R13 in series with saidreactances, and two arms comprising reactances X22 and X23 each in shuntwith a variable resistance R22 and R23 and connected in series with theshunt arm of said T, said reactances and resistances being relatedsubstantially a second pluralityT of impedances in series with eachother and with another arm of said base loss network, said secondimpedances each comprising reactance in parallel with a resistor whichis variable in inverse relation to the resistors contained in the firstmentioned impedances, said second impedances being inverse to said firstimpedances, said rst and second impedances and said base loss networkbeing arranged to form a lattice and to exhibit a constant imageimpedance in both directions of transmission for all values ofadjustments of the variable resistors.

3. In an equalizer having fixed resistances in a T conguration andhaving a predetermined iinite base loss and image impedance thecombination therewith of circuit elements for producing adjustableamounts of attenuation comprising variable resistances bridging the T,other varia-ble resistances in series with the pillar arm of said T,impedances in series with said first variable resistances, otherimpedances in shunt with said other variable resistances; saidimpedances being mutually inverse and said variable resistances beingmutually inverse for all values.

4. An adjustable attenuation equalizer for independently adjusting thetransmission loss over a plurality of ranges within a frequencyspectrum, said equalizer comprising a base lossnetwork having a givennite loss and a given image impedance, a plurality of impedances inshunt with each other and with an arm of the Abase loss network, each ofsaid impedances'comprisl ing reactance in series with a variableresistor, a second plurality of impedances in series with each other andwith another arm of said base loss network, said second impedances eachcomprising reactance in parallel with a resistor which is variable ininverse relation to the resistors contained in the rst mentionedimpedances, said second impedances being inverse to said iirstimpedances, said first and second impedances and said base loss networkbeing arranged to exhibit a constant image impedance in both directionsof transmission for all values of adjustments of the variable resistors,said iirst mentioned plurality of impedances and the arm of the baseloss network shunted thereby bridging a unity-ratio series-aidingtransformer, and said second plurality of impedances and the arm of theybase loss network in series .therewith being connected to the mid-pointof said transformer to form a pillar arm.

5. An adjustable attenuation equalizer for independently adjusting thetransmission loss over a plurality of ranges within a frequencyspectrum, said equalizer comprising a base loss network having a givennite loss and a given image impedance, a plurality of impedances inshunt with each other and with an arm of the base loss network, each ofsaid impedances comprising reactance in series with a variable resistor,a second plurality of impedances in series with each other and withanother arm of said base loss network, said second impedances eachcomprising reactance in parallel with a resistor which is variable ininverse relation to the resistors contained in the first mentionedimpedances, said second impedances being inverse to said rst impedances,said first and second impedances and said base loss network beingarranged to exhibit a constant image impedance in both directions oftransmission for all values of adjustments of the variable resistors.

6. An adjustable attenuation equalizer for independently adjusting thetransmission loss over a plurality of ranges within a frequencyspectrum, said equalizer comprising a base loss network having a givenfinite loss and a given image impedance, a plurality of impedances inshunt with each other and with an arm of the base network, each of saidimpedances comprising reactance in series with a variable resistor, asecond plurality of impedances in series with each other and withanother arm of said base loss network, said second impedances eachcomprising L reactance in parallel with a resistor which is Variable ininverse relation to the resistors contained in the rst mentionedimpedances, said second impedances being inverse to said firstimpedances, said iirst and second impedances and said base loss networkbeing arranged to exhibit a constant image impedance in both directionsof transmission for all Values of adjustments of the Variable resistors,said base loss network comprising a T, the rst mentioned im- ,f

pedances bridging the T, and the second impedances being in series withthe shunt arm of the T.

7. An adjustable attenuation equalizer for independently adjusting thetransmission loss over a plurality of ranges within a frequencyspectrum, said equalizer comprising a base loss network having a givennite loss and a given image impedance, a plurality of impedances inshunt with each and with an arm of the base loss network, each of saidimpedances comprising reactance in series with a variable resistor, asecond plurality ofimpedances in series with each other and with anotherarm of said base loss network, said second impedances each comprisingreactance in parallel with a resistor which is Variable in inverserelation to the resistors contained in the first mentioned impedances,said second impedances being inverse to said rst impedances, said firstand second impedances and said base loss network being arranged toexhibit a constant image impedance in both directions of transmissionfor all values of adjustments of the variable resistors, said base lossnetwork having an attenuation between 10 and 20 decibels.

8. A constant resistance variable attenuation equalizer comprising adissipative T network, two arms each comprising a reactance and avariable resistance in series and each arm bridging said T, and two armseach comprising a reactance and a Variable resistance in parallel, saidlast mentioned arms being connected in series with each other and withthe shunt arm of said T, said last mentioned arms being inverse to saidrst arms with respect to the image impedance of the network so that theproduct of each second arm with its corresponding rst arm is equal tothe` square of the image impedance of the network.

9. A constant resistance variable attenuation equalizer comprising adissipative T network, a plurality of arms each comprising a reactanceand a variable resistance in series and each of said arms bridging saidT, and a plurality of arms each comprising a reactance and a variableresistance in parallel, said last mentioned arms being connected inseries with each other and with the shunt arm of said T, said lastmentioned arms being inverse to said rst arms with respect to the imageimpedance of the network so that the product of each second arm with acorresponding rst arm is equal to the square of the image impedance ofthe network.

PAUL W. KLIPSCH.

